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Topological Rings
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Download or read book Topological Rings written by S. Warner and published by Elsevier. This book was released on 1993-07-07 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included. The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn's Lemma, is also expected.
Book Synopsis Topological Rings Satisfying Compactness Conditions by : M. Ursul
Download or read book Topological Rings Satisfying Compactness Conditions written by M. Ursul and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction In the last few years a few monographs dedicated to the theory of topolog ical rings have appeared [Warn27], [Warn26], [Wies 19], [Wies 20], [ArnGM]. Ring theory can be viewed as a particular case of Z-algebras. Many general results true for rings can be extended to algebras over commutative rings. In topological algebra the structure theory for two classes of topological algebras is well developed: Banach algebras; and locally compact rings. The theory of Banach algebras uses results of Banach spaces, and the theory of locally compact rings uses the theory of LCA groups. As far as the author knows, the first papers on the theory of locally compact rings were [Pontr1]' [J1], [J2], [JT], [An], lOt], [K1]' [K2]' [K3], [K4], [K5], [K6]. Later two papers, [GS1,GS2]appeared, which contain many results concerning locally compact rings. This book can be used in two w.ays. It contains all necessary elementary results from the theory of topological groups and rings. In order to read these parts of the book the reader needs to know only elementary facts from the theories of groups, rings, modules, topology. The book consists of two parts.
Book Synopsis Introduction to the Theory of Topological Rings and Modules by : V. Arnautov
Download or read book Introduction to the Theory of Topological Rings and Modules written by V. Arnautov and published by CRC Press. This book was released on 1995-11-30 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a thorough introduction to the theory of topological rings and modules--focusing on problems of topologization and extensions of ring topologies.
Book Synopsis Topological Groups by : R. V. Gamkrelidze
Download or read book Topological Groups written by R. V. Gamkrelidze and published by CRC Press. This book was released on 1987-03-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering the insights of L.S. Pontryagin, one of the foremost thinkers in modern mathematics, the second volume in this four-volume set examines the nature and processes that make up topological groups. Already hailed as the leading work in this subject for its abundance of examples and its thorough explanations, the text is arranged so that readers can follow the material either sequentially or schematically. Stand-alone chapters cover such topics as topological division rings, linear representations of compact topological groups, and the concept of a lie group.
Book Synopsis Topological Groups and the Pontryagin-van Kampen Duality by : Lydia Außenhofer
Download or read book Topological Groups and the Pontryagin-van Kampen Duality written by Lydia Außenhofer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-11-22 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to topological groups and the structure theory of locally compact abelian groups, with a special emphasis on Pontryagin-van Kampen duality, including a completely self-contained elementary proof of the duality theorem. Further related topics and applications are treated in separate chapters and in the appendix.
Book Synopsis Topological Groups and Related Structures by : A. V. Arkhangelʹskiĭ
Download or read book Topological Groups and Related Structures written by A. V. Arkhangelʹskiĭ and published by atlantis press. This book was released on 2008 with total page 797 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a large amount of material, both classic and recent (on occasion, unpublished) about the relations of Algebra and Topology. It therefore belongs to the area called Topological Algebra. More specifically, the objects of the study are subtle and sometimes unexpected phenomena that occur when the continuity meets and properly feeds an algebraic operation. Such a combination gives rise to many classic structures, including topological groups and semigroups, paratopological groups, etc. Special emphasis is given to tracing the influence of compactness and its generalizations on the properties of an algebraic operation, causing on occasion the automatic continuity of the operation. The main scope of the book, however, is outside of the locally compact structures, thus distinguishing the monograph from a series of more traditional textbooks.The book is unique in that it presents very important material, dispersed in hundreds of research articles, not covered by any monograph in existence. The reader is gently introduced to an amazing world at the interface of Algebra, Topology, and Set Theory. He/she will find that the way to the frontier of the knowledge is quite short -- almost every section of the book contains several intriguing open problems whose solutions can contribute significantly to the area.
Download or read book Topological Fields written by S. Warner and published by Elsevier. This book was released on 1989-06-01 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at those acquainted with basic point-set topology and algebra, this text goes up to the frontiers of current research in topological fields (more precisely, topological rings that algebraically are fields).The reader is given enough background to tackle the current literature without undue additional preparation. Many results not in the text (and many illustrations by example of theorems in the text) are included among the exercises. Sufficient hints for the solution of the exercises are offered so that solving them does not become a major research effort for the reader. A comprehensive bibliography completes the volume.
Book Synopsis Basic Topology 2 by : Avishek Adhikari
Download or read book Basic Topology 2 written by Avishek Adhikari and published by Springer Nature. This book was released on 2022-09-08 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second of the three-volume book is targeted as a basic course in topology for undergraduate and graduate students of mathematics. It focuses on many variants of topology and its applications in modern analysis, geometry, algebra, and the theory of numbers. Offering a proper background on topology, analysis, and algebra, this volume discusses the topological groups and topological vector spaces that provide many interesting geometrical objects which relate algebra with geometry and analysis. This volume follows a systematic and comprehensive elementary approach to the topology related to manifolds, emphasizing differential topology. It further communicates the history of the emergence of the concepts leading to the development of topological groups, manifolds, and also Lie groups as mathematical topics with their motivations. This book will promote the scope, power, and active learning of the subject while covering a wide range of theories and applications in a balanced unified way.
Book Synopsis The Classical Fields by : H. Salzmann
Download or read book The Classical Fields written by H. Salzmann and published by Cambridge University Press. This book was released on 2007-08-23 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The real, rational, complex and p-adic numbers are discussed in detail in this comprehensive work.
Author :Alexander Arhangel’skii Publisher :Springer Science & Business Media ISBN 13 :949121635X Total Pages :794 pages Book Rating :4.4/5 (912 download)
Book Synopsis Topological Groups and Related Structures, An Introduction to Topological Algebra. by : Alexander Arhangel’skii
Download or read book Topological Groups and Related Structures, An Introduction to Topological Algebra. written by Alexander Arhangel’skii and published by Springer Science & Business Media. This book was released on 2008-05-01 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.
Book Synopsis Topological Rings and Infinite Matrices by : Wilbur Leonard Mitchell
Download or read book Topological Rings and Infinite Matrices written by Wilbur Leonard Mitchell and published by . This book was released on 1940 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Rings of Sets and the Theory of Vector Measures by : V. M. Bogdan
Download or read book Topological Rings of Sets and the Theory of Vector Measures written by V. M. Bogdan and published by . This book was released on 1978 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elementary Concepts of Topology by : Paul Alexandroff
Download or read book Elementary Concepts of Topology written by Paul Alexandroff and published by Courier Corporation. This book was released on 2012-08-13 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis Equational Compactness in Rings by : D. K. Haley
Download or read book Equational Compactness in Rings written by D. K. Haley and published by Springer. This book was released on 2006-11-15 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis L.S. Pontryagin Selected Works: Topological groups by : Lev Semenovich Pontri︠a︡gin
Download or read book L.S. Pontryagin Selected Works: Topological groups written by Lev Semenovich Pontri︠a︡gin and published by . This book was released on 1986 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Reviews of Papers in Algebraic and Differential Topology, Topological Groups, and Homological Algebra by : Norman Earl Steenrod
Download or read book Reviews of Papers in Algebraic and Differential Topology, Topological Groups, and Homological Algebra written by Norman Earl Steenrod and published by . This book was released on 1968 with total page 890 pages. Available in PDF, EPUB and Kindle. Book excerpt:
